Activation lock and account locked on iPad 2

Given what you have told us, there is nothing you can do now. If it is some consolation, an iPad2 is almost unusable these days since as you observe, it is 12 years old. I have 2 that are waiting for my next trip to an Apple store (for recycling).

Next time, make sure you keep note of those "randomized" bits of information.

read this section from the very bottom of Apple Trade In - Apple :

"Does Apple offer recycling?

Yes. Apple Trade In lets you recycle any Apple device (including devices from Apple-owned brands) at any Apple Store and on Apple for free. That includes your batteries and old electronic products as well as free, on-demand packaging recycling for our commercial, education, and institutional customers. When we receive your device, it will be thoroughly inspected to determine if components can be recycled or reused. Whether recycled or reused, all activities relating to the processing of your device will be managed in an environmentally responsible way."

Without access to your account that was used to sign into the device, the Activation Lock removal request is the only solution. Having the original receipt is what has been seen as required for Proof of Ownership, and usually the receipt needs to be from Apple or Authorized Apple seller. There is no date or serial number lookup method to find your Purchase Receipt.

When purchased online, you may be able to view the invoice of the purchase, but you would need the Apple Account/Password used for that purchase and of course need access to that account, so that option is not available either. That means you would have had to save the original purchase receipt yourself.

Keep your receipt after you buy an Apple device - Apple Support

As you have found the so called "removal" tools do not work, and there is no way to bypass the Activation Lock.